Number dictionary · Exact arithmetic
1024: factors and number facts
one thousand twenty-four is an even number and is composite. Its 11 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand twenty-four
- Roman numeral
- MXXIV
- Prime factorization
- 2^10
- Digital root
- 7
All factors of 1024
A positive factor divides 1024 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
Factor pairs
- 1 × 1024 = 1024
- 2 × 512 = 1024
- 4 × 256 = 1024
- 8 × 128 = 1024
- 16 × 64 = 1024
- 32 × 32 = 1024
Each pair describes an arrangement of 1024 items into equal rows. The 32 × 32 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 11
- Sum of all divisors
- 2047
- Sum excluding 1024
- 1023
- Classification
- deficient
1024 is deficient because its proper divisors add to 1023, which is less than 1024.
Prime factorization of 1024
1024 = 2^10
Repeated division, step by step
- 1024 ÷ 2 = 512
- 512 ÷ 2 = 256
- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
Multiply the prime divisors in these steps to reconstruct 1024. An exponent records how many times the same prime occurs. The divisor-count calculation is (10 + 1) = 11.
The preceding prime is 1021. The next larger prime is 1031. The factor list above explains why 1024 is composite.
Learn the factorization method1024 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand twenty-four |
| Roman numeral | MXXIV |
| Binary (base 2) | 10000000000 |
| Octal (base 8) | 2000 |
| Decimal (base 10) | 1024 |
| Hexadecimal (base 16) | 400 |
Check the binary conversion
Read 10000000000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 = 1024
Check the hexadecimal conversion
4 × 16^2 + 0 × 16^1 + 0 × 16^0 = 1024
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 1024
- 1024 squared
- 1024 × 1024 = 1,048,576
- 1024 cubed
- 1024 × 1024 × 1024 = 1,073,741,824
- Square root
- = 32
- Simplified radical
- 32
1024 is a perfect square: 32 × 32 = 1024. It is not a perfect cube.
1024 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1024.
Distinguish a square from a square rootMultiplication table for 1024
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 512 | 0 | Yes |
| 3 | 341 | 1 | No |
| 4 | 256 | 0 | Yes |
| 5 | 204 | 4 | No |
| 6 | 170 | 4 | No |
| 7 | 146 | 2 | No |
| 8 | 128 | 0 | Yes |
| 9 | 113 | 7 | No |
| 10 | 102 | 4 | No |
| 11 | 93 | 1 | No |
| 12 | 85 | 4 | No |
For example, 1024 = 7 × 146 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1024
1024 contains 4 decimal digits. Its digit sum is 1 + 0 + 2 + 4 = 7.
- 1024: 1 + 0 + 2 + 4 = 7
The digital root is 7. Reversing its digits gives 4201; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 1024/100 simplifies to 256/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 10.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1024 and 12 is 4. Their least common multiple is 3072. The identity GCD × LCM = 1024 × 12 = 12288 checks both results.
Work through GCF and LCMQuestions about 1024
What are the factors of 1024?
The positive factors are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. There are 11 factors, including 1 and 1024.
Is 1024 a prime number?
No. 1024 is composite: 2^10 = 1024.
How do you write 1024 in Roman numerals?
1024 is MXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 1024?
1024 in decimal is 10000000000 in base 2. Adding its active place values gives 1024 = 1024.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 1024
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1024 add to 7. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.